The discussion revolves around proving the identity cosh(2x) = cosh²(x) + sinh²(x), utilizing the definitions of hyperbolic sine and cosine functions.
Some participants have provided guidance on expanding the squares of the binomials, while others express their confusion about the process. There is a mix of attempts to clarify the steps involved.
Participants are working within the constraints of homework expectations, which may limit the type of assistance they can provide to one another.
J.live said:Homework Statement
Prove
cosh(2x)= cosh^2(x) + sinh^2(x)
Homework Equations
sinh(x) ≡ [ e^(x) - e^(-x) ] / 2
cosh(x) ≡ [ e^(x) + e^(-x) ] / 2
The Attempt at a Solution
= { [ e^(x) + e^(-x) ] / 2 }² + { [ e^(x) - e^(-x) ] / 2 }²
= [ e^(x) + e^(-x) ]² / 2² + [ e^(x) - e^(-x) ]² / 2²
... gets confusing after this. Thanks in advance.
J.live said:confusing